Escape Rates of Externally Confined Polymers

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Harri Mökkönen Name of the doctoral dissertation Escape Rates of Externally Confined Polymers: Publisher School of Science Unit Department of Applied Physics Series Aalto University publication series DOCTORAL DISSERTATIONS 143/2016 Field of research Theoretical and computational physics Manuscript submitted 17 May 2016 Date of the defence 19 August 2016 Permission to publish granted (date) 28 June 2016 Language English Monograph Article dissertation Essay dissertation Abstract A polymer escaping from a confining external potential represents a generic description of long macromolecules crossing an energy barrier. This type of barrier crossing problems are typical in nanoand microscale polymeric systems, where the polymers are escaping from entropic traps by thermal fluctuations. These systems have possible bioengineering applications, where they can be for example used in sorting polymers. In this thesis, polymer escape from oneand two-dimensional external potentials was studied theoretically and computationally. In a two-dimensional asymmetric external potential, the escape rate of a polymer was solved using Path Integral Hyperdynamics (PIHD) simulations and Kramers' theory using effective potentials for different lengths of polymers. We found that Kramers' theory predicts the escape rate of PIHD simulations qualitatively but the prediction agrees quantitatively only for shorter chains. We also determined that a one-dimensional reaction coordinate is not sufficient to describe the dynamics of the longer polymer chains. In a one-dimensional symmetric double-well external potential, the escape rate was solved using Langevin dynamics simulations, Brownian dynamics simulations, harmonic transition state theory (HTST) with dynamical corrections (DC), Langer's theory, and Forward flux sampling (FFS). FFS and HTST with DC both predict the rate by Langevin and Brownian dynamics simulations quantitatively within a factor of two. We also introduced a new method for computing dynamical corrections using forward flux sampling type of algorithm and compared computational efficiency of the different methods.A polymer escaping from a confining external potential represents a generic description of long macromolecules crossing an energy barrier. This type of barrier crossing problems are typical in nanoand microscale polymeric systems, where the polymers are escaping from entropic traps by thermal fluctuations. These systems have possible bioengineering applications, where they can be for example used in sorting polymers. In this thesis, polymer escape from oneand two-dimensional external potentials was studied theoretically and computationally. In a two-dimensional asymmetric external potential, the escape rate of a polymer was solved using Path Integral Hyperdynamics (PIHD) simulations and Kramers' theory using effective potentials for different lengths of polymers. We found that Kramers' theory predicts the escape rate of PIHD simulations qualitatively but the prediction agrees quantitatively only for shorter chains. We also determined that a one-dimensional reaction coordinate is not sufficient to describe the dynamics of the longer polymer chains. In a one-dimensional symmetric double-well external potential, the escape rate was solved using Langevin dynamics simulations, Brownian dynamics simulations, harmonic transition state theory (HTST) with dynamical corrections (DC), Langer's theory, and Forward flux sampling (FFS). FFS and HTST with DC both predict the rate by Langevin and Brownian dynamics simulations quantitatively within a factor of two. We also introduced a new method for computing dynamical corrections using forward flux sampling type of algorithm and compared computational efficiency of the different methods.